\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(f : [0, +\infty[ \to [0, +\infty[\), \(f(x) = x^2\). Show \(f\) is bijective and continuous, \(f'\) does not vanish on \(]0, +\infty[\), and apply the inverse-map derivative formula to recover \((\sqrt{y})' = 1/(2 \sqrt{y})\) on \(]0, +\infty[\).
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